Block #1,423,760

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/22/2016, 11:07:11 AM · Difficulty 10.7757 · 5,412,995 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
7ad1e79dd2f74dcf85646b0c00fdb4f4d7660bfab02a45d04cecf6c0195715da

Height

#1,423,760

Difficulty

10.775709

Transactions

2

Size

733 B

Version

2

Bits

0ac694da

Nonce

1,811,811,040

Timestamp

1/22/2016, 11:07:11 AM

Confirmations

5,412,995

Merkle Root

c5c66f15b51912dec25e8eebd7588a691c76f9b0d56815d7a979edd54a3fbd50
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.114 × 10⁹⁴(95-digit number)
31141333191538595606…09183286739322923761
Discovered Prime Numbers
p_k = 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
3.114 × 10⁹⁴(95-digit number)
31141333191538595606…09183286739322923761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.228 × 10⁹⁴(95-digit number)
62282666383077191213…18366573478645847521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.245 × 10⁹⁵(96-digit number)
12456533276615438242…36733146957291695041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.491 × 10⁹⁵(96-digit number)
24913066553230876485…73466293914583390081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.982 × 10⁹⁵(96-digit number)
49826133106461752970…46932587829166780161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.965 × 10⁹⁵(96-digit number)
99652266212923505941…93865175658333560321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.993 × 10⁹⁶(97-digit number)
19930453242584701188…87730351316667120641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.986 × 10⁹⁶(97-digit number)
39860906485169402376…75460702633334241281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.972 × 10⁹⁶(97-digit number)
79721812970338804753…50921405266668482561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.594 × 10⁹⁷(98-digit number)
15944362594067760950…01842810533336965121
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,938,327 XPM·at block #6,836,754 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy Policy·

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy